Thermodynamics and Thermochemistry - Result Question 64
64. One mole of an ideal gas is taken from $a$ to $b$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $W _s$ and that along the dotted line path is $W _d$, then the integer closest to the ratio $W _d / W _s$ is
(2010)
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Answer:
Correct Answer: 64. $(2)$
Solution:
Work done along dashed path $|-W|=\Sigma p \Delta V$
$ =4 \times 1.5+1 \times 1+\dfrac{2}{3} \times 2.5=8.65 $ $L$ $ atm $
Work done along solid path $-W=n R T \ln \dfrac{V _2}{V _1}=p _1 V _1 \ln \dfrac{V _2}{V _1}$
$ =2 \times 2.3 \log \dfrac{5.5}{0.5}=2 \times 2.3 \log 11=4.79 $
$ \Rightarrow \dfrac{W _d}{W _s}=\dfrac{8.65}{4.79}=1.80 \approx 2 $
BETA
